Ben Wilkinson's side were greeted with strong, windy conditions on Merseyside, so an early goal would be crucial to asserting control in the game.
And that is exactly what City got when, just five minutes in, striker Dickson found himself free inside the box and made no mistake by clinically guiding the ball past Fabian Mrozek.
The away side remained firmly in control of the game throughout the first period, adapting well to the tricky conditions on Merseyside, restricting the home side to few opportunities, while being able to break through their high press with relative ease.
And we could have doubled our lead when winger Liam Smith found himself through on goal, striking a left-footed effort against the woodwork, meaning we had to settle for a one-goal lead going into half-time.
Following the break, City again had a great chance to double our advantage, when some nice link-up play down the right with Adedire Mebude gave Rico Lewis some space inside the area. The full-back lashed at goal but it was palmed away by Liverpool keeper Mrozek.
City kept knocking on the door in search for a second, with Liam Smith and Mebude consistently posing a threat down the flanks.
And we eventually doubled our lead when Nico O'Reilly picked the ball up from Kian Breckin inside our own half, driving forward before sliding the ball through to Smith who fired home a wonderfully work goal past Mrozek.
HOW WE LINED UP
WHAT IT MEANS
With a win and a draw against Aston Villa and Crystal Palace respectively in our opening two Premier League Cup games, this win over Liverpool means City have now guaranteed their place in the quarter-finals of the U18 Premier League Cup.
It is not long until we see the U18s back in action, as they will take on Nottingham Forest in the U18 Premier League at the City Football Academy next week.
Kick-off is at 1pm (UK) on Wednesday 1 December.
News about Liverpool v Man City
Match Highlights: Liverpool U18s 0-2 City U18s
Manchester City Under 18s’ secured qualification to the quarter-finals of the U18 Premier League Cup thanks to a 2-0 win over Liverpool. Watch more.
Full Match Replay: Liverpool U18s v City U18s
Relive every kick of our U18 Premier League Cup clash with Liverpool on CITY+. Watch more.